We consider a non-linear Hartree energy for bosonic particles in a symmetric double-well potential. In the limit where the wells are far apart and the potential barrier is high, we prove that the ground state and first excited state are given to leading order by an even, respectively odd, superposition of ground states in single wells. The corresponding energies are separated by a small tunneling term that we evaluate precisely.

中文翻译：

---

双井中的 Hartree 函数

我们考虑对称双阱势中玻色子粒子的非线性 Hartree 能量。在井相距很远且势垒高的极限下，我们证明了基态和第一激发态通过单井中基态的偶数和奇数叠加给予先导顺序。相应的能量由我们精确评估的小隧道项分开。